Questions tagged [approximation]

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2
votes
2answers
2k views

z-Transform Methods: Definition vs. Integration Rule

The definition of the z-transform is defined as $z = e^{sT}$ where "s" is complex frequency for continuous-time systems and "T" is the sample period. Why are rules such as the forward rectangular ...
27
votes
5answers
17k views

What Is the Best First Order IIR (AR Filter) Approximation to a Moving Average Filter (FIR Filter)?

Assume the following first order IIR Filter: $$ y[n] = \alpha x[n] + (1 - \alpha) y[n - 1] $$ How can I choose the parameter $ \alpha $ s.t. the IIR approximates as good as possible the FIR which is ...
1
vote
2answers
1k views

Kaiser window approximation

Are there any "good" low-computational-cost approximations for parameterized Kaiser window generation suitable for small systems/languages that do not include Bessel functions in their standard ...
15
votes
2answers
13k views

Using continuous verses discrete wavelet transform in digital applications

I am familiar with much of the mathematical background behind wavelets. However when implementing algorithms on a computer with wavelets I am less certain about whether I should be using continuous or ...
3
votes
2answers
667 views

Pade Approximation of dead time

For the time delay $e^{-sT}$ I shall find the Pade Approximation for $M = 0$ and $N = 1$. $f(s) = \sum_i^{\infty} a_is^i \approx \dfrac{\sum_{n=0}^{N} b_is^i}{\sum_{m=0}^{M} c_is^i}$ $e^{-sT} = \...
2
votes
1answer
415 views

Wavelet transform: How to compute the initial coefficients when only samples are available?

In standard MRA we have that the space of functions at scale J can be expressed as $$V_j = V_0\oplus \left(\bigoplus_{j=0}^{J} W_j\right)$$ where $V_0$ is spanned by the orthonormal system of the ...
0
votes
1answer
87 views

Self study question about Padé Approximation and transfer functions

Given a signal $x[n] = [1, 2, 3, 4, 5]$. How many transfer functions can be found with Padé approximation which have a causal impulse response and start with those five samples. How many of them are ...